Solve for $x$ : $2x^2 - 2x - 112 = 0$
Explanation: Dividing both sides by $2$ gives: $ x^2 {-1}x {-56} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-56$ , so we need to find two numbers that add up to $-1$ and multiply to $-56$ The two numbers $7$ and $-8$ satisfy both conditions: $ {7} + {-8} = {-1} $ $ {7} \times {-8} = {-56} $ $(x + {7}) (x {-8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 7) (x -8) = 0$ $x + 7 = 0$ or $x - 8 = 0$ Thus, $x = -7$ and $x = 8$ are the solutions.